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The Replica Symmetric Solution for Potts Models on d-Regular Graphs

Dembo, Amir; Montanari, Andrea; Sly, Allan; Sun, Nike


We establish an explicit formula for the limiting free energy density (log-partition function divided by the number of vertices) for ferromagnetic Potts models on uniformly sparse graph sequences converging locally to the d-regular tree for d even, covering all temperature regimes. This formula coincides with the Bethe free energy functional evaluated at a suitable fixed point of the belief propagation recursion on the d-regular tree, the so-called replica symmetric solution. For uniformly...[Show more]

CollectionsANU Research Publications
Date published: 2014
Type: Journal article
Source: Communications in Mathematical Physics
DOI: 10.1007/s00220-014-1956-6


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